Solve for $x$ : $x^2 - 8x + 15 = 0$
The coefficient on the $x$ term is $-8$ and the constant term is $15$ , so we need to find two numbers that add up to $-8$ and multiply to $15$ The two numbers $-3$ and $-5$ satisfy both conditions: $ {-3} + {-5} = {-8} $ $ {-3} \times {-5} = {15} $ $(x {-3}) (x {-5}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x -3) (x -5) = 0$ $x - 3 = 0$ or $x - 5 = 0$ Thus, $x = 3$ and $x = 5$ are the solutions.